Statistics
In basketball (as well as all other team sports) statistics play an important
role. They can show how good a player or a team is, give clues as
to strengths and weaknesses of a team, and explain why a team won or lost
a given game. However, they can often give misleading information if not
looked at carefully.
3 rules of statistics
There are three basic rules of gathering and examining statistics:
relative and absolute data, amount of data, and same unit calculations.
Relative and Absolute data
Although relative data can sometimes distort a picture, it can often clear
it up. For example, take two imaginary players, Milton and Bradley.
Milton has played in 20 games and scored 10 points in each game, for a
total of 200 points. Bradley has played in 100 games and scored 2 points
in each game, for a total of 200 points. Looking at their totals (200 points
each), it seems that they are of about equal ability. However, it is easily
seen that Milton is the far better player. That is why one should always
use averages in similar calculations, so that it can be clearly seen who
really is the better player.
Amount of data
There's no knowing what combination of heads and tails you got!
The "expected" result is 5 heads and 5 tails, because there is equal probability
of either happening. However, you may have gotten 6-4, 3-7, or any other
combination. Remember: probability is chance, not laws. Now, try flipping
the above coin 10 or 20 more times. Chances are that it's closer to the
expected result. That is because the more data you have, the more accurate
the result. In basketball, this rule also applies. For example, using the
rating system described below, Michael Jordan (Chicago Bulls) has a rating
of 33.4. Shaquille O'Neal (LA Lakers) has a rating of 42.2.
Most people would agree that Shaquille O'Neal is not better than Michael
Jordan, and even those who believe that he is better agree that he is not
better by that much. A closer look at the statistics reminds us of several
things. Below is a table of some important totals for these players during
the 96-97 NBA regular season.
| Name |
Games |
Points |
Rebounds |
Assists |
| Jordan, Michael |
82 |
2431 |
482 |
352 |
| O'Neal, Shaquille |
51 |
1336 |
640 |
159 |
Obviously, since O'Neal played less games, his totals are less. However,
if you find the averages for the players, a different picture forms.
Below are the same stats, except that instead of totals, there are season
averages in the points, rebounds, and assists column.
| Name |
Games |
Points per game |
Rebounds per game |
Assists per game |
| Jordan, Michael |
82 |
29.6 |
5.9 |
4.3 |
| O'Neal Shaquille |
51 |
26.1 |
12.5 |
3.1 |
These stats show that the two players are nearly equal in points and
assists per game, but Jordan has a huge disadvantage in the rebounds column.
Most basketball fans would notice that something is wrong. Shaquille O'Neal's
scoring average (26.1) was very much affected by the several good games
he had after his return. In this manner, his averages were affected more
than they should have been. For example, in an NBA season our imaginary
player Milton has a scoring average of 20.0 points per game (ppg) after
playing in 81 of the 82 games of the regular season. That means that he
scored a total of 1620 points this season. Our second imaginary player
Bradley also has an average of 20.0 ppg, but he was injured half of the
season and only played 40 games, which means that he has a total of 800
points. In the last (82nd) game of the season, the two players meet in
a game and each one scores an incredible 60 points. After such a performance,
Milton's average rises to 20.5 points. Bradley's average, however, rises
to 21.0 points. This gives the impression that Bradley is much better than
Milton, although they are almost exactly equal in ability. This shows that
a good performance benefits a player who has played less games more than
a player who has played more games, and very well illustrates the second
rule of statistics: the more data you have, the more accurate the results.
At first, it seems that this rule goes against rule #1 (take averages,
not totals), but that is untrue. The best solution is to find the averages
of Milton and Bradley over the past several years. That way, you will have
an average representation, and you will receive the benefit of having more
accurate data because it's "evened out" by the amount of data.
Same unit calculations
In areas such as basketball, one has many different statistics to deal
with. Is the best player the one with the most points? The most rebounds?
The most steals? In areas where there are many different types of data,
it is important to convert all of the data to the same unit. Points, rebounds,
assists, steals, turnovers, missed shots and fouls are some of the stats
that each player has. For use on this site, we have developed a formula
to give each player a rating, which may be used to compare him to other
players and to find team ratings. This rating is a number indicating how
many points is a player worth to his team. What follows is a step-by-step
breakdown of each part of the formula.
Positives
Points-Since our unit of choice is points, we have to stick to it.
Each point is worth one rating point.
Rebounds-An offensive rebound gives a good opportunity for scoring,
and a defensive one takes away an opponent's chance of scoring. It's not
worth 2 points because it's a chance that the opponent or you will
score. It is not a 2 point basket that is being scored/taken away from
opponent, it's a chance at one. Therefore, each rebound is worth
1.5 rating units.
Assists-An assist means that the player directly helped his
team to score, so each assist is worth 2 rating points (a basket is usually
worth 2 points).
Steals-A steal gives the team a chance to score, so it
is worth 1.5 rating points.
Blocks-A block should be worth the same amount of points as
a rebound. However, it should be remembered that unsuccessful blocks sometimes
alter a shot a little, often enough for it to miss its mark. That is why
blocks are worth 2 rating points.
Negatives
Turnovers-Just like a steal gains a chance at a shot, a turnover
gives it up. Therefore, turnovers are worth -1.5 rating points.
Personal Fouls-A foul not only gives the other team a possible
chance to shoot foul shots, 6 fouls in one game mean that the player is
disqualified for the rest of the game. Also, most coaches will not keep
a player with 4 or 5 fouls in the game until the last minute, for fear
that the player may get another foul and be disqualified. That is why a
foul is worth -2 rating points.
Shots Missed-A missed shot gives the other team a chance for
a rebound and score, as well as not scoring. However, offensive rebounds
make up for that miss. Each missed shot that is not rebounded by the same
player has a 50-50 chance of being rebounded by either team. So then the
difference [Missed Shots-Offensive Rebounds] is worth -1 ratings point.
Final Rating Formula
So, after all the factors are added/subtracted, the final formula is:
{ [(points)+(rebounds*1.5)+(Assists*2)+(Steals*1.5)+(Blocks*2)]-[(Turnovers*1.5)+(Fouls*2)+(Shots
Missed-Offensive Rebounds)] }/Games Played
Now that you know all the principles of statistics, why don't you pick
two (W)NBA teams and have some fun seeing who wins, in our Game Predicter game. But remember, the results given are far from the truth, because of the fact that team ratings are simply the average of the players on the team, and don't in any way reflect reality, because of injuries and the above-described factors.
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